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A067142
One half of the number of Young tableaux with n cells whose shape is asymmetric.
2
0, 0, 1, 1, 4, 10, 30, 106, 316, 1254, 4140, 17128, 63856, 271492, 1126216, 4936608, 22278712, 101330506, 487735440, 2313734596, 11706759352, 58073844300, 305941244576, 1587272257096, 8656011151184, 46886237603400, 263791190603200, 1487539434072976
OFFSET
0,5
COMMENTS
Equivalently, the row lengths are a non-self-conjugate partition of n.
FORMULA
a(n) = (A000085(n) - A067136(n))/2.
a(n) = A330645(n)/2. - Omar E. Pol, Jan 11 2020
EXAMPLE
a(4) = 4 = 8/2; the 8 tableaux are:
1..1234..123..124..134..14..12..13
2........4....3....2....2...3...2.
3.......................3...4...4.
4.................................
The two tableaux of size 4 with symmetric shape are excluded:
12..13
34..24
CROSSREFS
KEYWORD
nonn
AUTHOR
Naohiro Nomoto, Feb 19 2002
EXTENSIONS
Edited by Franklin T. Adams-Watters, Nov 07 2006
a(26)-a(27) from Omar E. Pol, Jan 11 2020
STATUS
approved